A Fast in Silico Simulation of Ion Flux through the Large-Pore Channel Proteins  Sharron Bransburg-Zabary, Esther Nachliel, Menachem Gutman  Biophysical Journal  Volume 83, Issue 6, Pages 3001-3011 (December 2002) DOI: 10.1016/S0006-3495(02)75306-X Copyright © 2002 The Biophysical Society Terms and Conditions

Figure 1 Propagation of a particle along a flat schematic trajectory in the absence and presence of an external electric field. The left panels were calculated for a 40-Å-long trajectory having no internal electric field and constant entropic terms (top panel). The mid-panel depicts the eviction dynamics of a single particle, irreversibly injected at the left side of the trajectory (Z=−20) and irreversibly absorbed on the right side (Z=20). The accumulation of the particle's probability density past the exit port is presented as a function of the number of random steps taken by the system. The bottom panel depicts the probability density along the trajectory after N1/2 random steps. The right panel depicts the same features under a driving potential of 100mV (4 kBT). Biophysical Journal 2002 83, 3001-3011DOI: (10.1016/S0006-3495(02)75306-X) Copyright © 2002 The Biophysical Society Terms and Conditions

Figure 2 Propagation of a particle along a schematic trajectory having an internal electrostatic gradient in the absence of external electric field. Three systems are under investigation, all having a single potential minimum of 4 kBT, but the location varies in place, as indicated by the letters A–C. The middle panel depicts the eviction dynamics; the accumulation of the particle's probability density past the exit port is presented as a function of the number of random steps taken by the system. Please note that the curves calculated for systems B and C are practically identical, and significantly faster than the dynamics of system A. The bottom panel presents the probability density along the channel after N1/2 random steps. Biophysical Journal 2002 83, 3001-3011DOI: (10.1016/S0006-3495(02)75306-X) Copyright © 2002 The Biophysical Society Terms and Conditions

Figure 3 Propagation of a particle along a schematic trajectory having an uneven entropy term in the absence of an external electric field. Three systems are under investigation and differ in the distribution of the entropy term (Si value) along the trajectory. The shape of the Si function along the trajectory is presented in the top panel, the eviction dynamics in the middle panel, and the probability density profile for the three systems after N1/2 random steps is given in the bottom panel. Biophysical Journal 2002 83, 3001-3011DOI: (10.1016/S0006-3495(02)75306-X) Copyright © 2002 The Biophysical Society Terms and Conditions

Figure 4 The electrostatic potential maps of cross-sections along the PhoE channel. The electrostatic potentials were calculated by the DelPhi program using the detailed structure of the protein and ionic strength of a 1M solution of 1:1 electrolyte. The maps are presented sequentially, starting from the extracellular side (Z=−20) at 4-Å intervals toward the periplasmic side. Biophysical Journal 2002 83, 3001-3011DOI: (10.1016/S0006-3495(02)75306-X) Copyright © 2002 The Biophysical Society Terms and Conditions

Figure 5 The profile of the electrostatic potential along the trajectories calculated for negative (top frame) and positive (bottom frame) particles along the PhoE channel. The dotted and continuous lines represent, respectively, the potentials as calculated before and after the insertion of an explicit Cl− anion at the site of Z=8. For details see text. Biophysical Journal 2002 83, 3001-3011DOI: (10.1016/S0006-3495(02)75306-X) Copyright © 2002 The Biophysical Society Terms and Conditions

Figure 6 The most probable trajectories for ion passage through the PhoE, OmpF, and the WT form of the R. blastica general purpose porin (1PRN). The trajectories are presented as spheres (R=1Å) colored in red for negative particles and blue for positive ones. Below each image is the electrostatic potential profile calculated for a 1M solution of 1:1 electrolyte and an external field of −100mV (PhoE and OmpF) or −20mV (1PRN). The potential of the periplasmic side is set at 0. Biophysical Journal 2002 83, 3001-3011DOI: (10.1016/S0006-3495(02)75306-X) Copyright © 2002 The Biophysical Society Terms and Conditions

Figure 7 Propagation dynamics of positive and negative particles through the PhoE channel under a 100mV driving potential. The scenario is divided into four cases. Panels A and B depict the eviction dynamics of negative and positive particles moving through the channel protein in one orientation of the protein across the membrane, while frames C and D are the fluxes for the reverse orientation of the protein. Frames A and C depict the dynamics calculated for a negative particle. Frames B and D are for a positive particle. The ordinates denote the accumulation of the probability density past the exit ports and the abscissa is the number of random steps. Under each of the frames depicting the dynamics is the profile (in kT units) of the electrostatic potential along the trajectory. Biophysical Journal 2002 83, 3001-3011DOI: (10.1016/S0006-3495(02)75306-X) Copyright © 2002 The Biophysical Society Terms and Conditions